It is hard to know what Wigan Athletic could have done to stop Craig Bellamy in this mood. Drown him in a vat of Gaviscon perhaps, because there is no more caustic striker in the Premiership.

Bellamy, at his most influential, is a perpetual irritant, rising up like bile from the gut to cause maximum discomfort. He exists on impertinent sprints, mordant backchat and splenetic waves of his arm at any referee or linesman who finds against him. He scored the first two goals and set up the third. He might just save Liverpool's Premiership season. He is unlikely to save their souls.

This game will be presented as Bellamy's celebration of innocence. He was cleared of two assault charges at Cardiff magistrates' court last week, where the judge described the evidence against him as "a shambles" and the not-guilty verdict, 10 months after an alleged incident in a Cardiff nightclub, unburdened him. As songs of innocence go, though, it was not quite William Blake. He does not do happy gambolling. As far as football goes, his court appearance has not encouraged an overwhelming respect for authority.

It was Bellamy's brilliance which delivered Liverpool's first goals from open play, away from Anfield, in the Premiership all season. But the term "open play" does not really fit. He does not play openly. He skirmishes, niggling away on a defender's shoulder and in the grey areas of the laws. His boundless energy and ambition gave Liverpool a cutting edge, and suggested that Rafael Benítez's gamble on his dubious history might yet be rewarded, but much of it carries a disagreeable air.

Matt Jackson, Wigan's brawny central defender, was given the runaround and was lucky not to be replaced before half-time. Bellamy repeatedly sprinted clear, shoulders hunched as if wearing an American linebacker's padding, before Jackson's brain had even clicked into gear.

There can be no more galling experience in the Premiership. Bellamy does not defeat an adversary with respect and humility, as one of Liverpool's greatest strikers and another Welshman, Ian Rush, was wont to do, but cuts him down like a two-bit mafia hitman, then returns to backchat over the body.

Wigan's flat and ponderous back four had seemed likely to be tripped by Bellamy long before he gave Liverpool a ninth-minute lead. Jackson was left flat-footed by Emmerson Boyce's inadvertent backheader and Bellamy slipped away, expertly chipping over Chris Kirkland.

Jackson's woeful attempt to play offside gave Liverpool a second, Bellamy streaking on to Steven Gerrard's pass and this time beating Kirkland with a low finish. The third owed much to Gerrard's prodigious surge through midfield and pass to Bellamy, who crossed low from the left for Dirk Kuyt to finish. Kuyt would have been rested had not Peter Crouch been injured and until then he had been entirely overshadowed. The fourth summed up Wigan's afternoon, Gerrard crossing from the right and the ball deflecting past Kirkland off the knee of Lee McCulloch. Even then Bellamy, who took away two defenders, played a part.

Wigan could point to three good chances spurned. Before half-time McCulloch volleyed over from five yards after José Reina had palmed aside Paul Scharner's header. In the last 10 minutes, Emile Heskey hit a post and the ball ricocheted wide off David Cotterill's knees, and David Wright sidefooted over.

But the memory was of Bellamy's first-half display. He let rip at John Arne Riise for not playing a pass into the area he wished; he berated the referee, Mike Riley, for penalising him for a foul on Jackson, Riley responding with the benign smile that a kindly grandfather gives a recalcitrant child; he entirely missed Benítez's urging for him to angle his runs because, caught offside, he was too busy railing at the linesman.

Predictably, he was booked, for an off-the-ball kick at Leighton Baines. Many managers would have substituted him immediately, cashing in their winning chips while they could. Benítez kept him on, as if to demand that he showed maturity. He did, but can it last the season?

Man of the match Craig Bellamy

Bellamy's insistent and abrasive display shook Liverpool out of their away-day lethargy.

Best moment His presence of mind to square the ball for the third goal when he was blowing so hot that a selfish attempt at a hat-trick would have been unsurprising.